The Influence of Volumetric Tumor Doubling Time, DNA Ploidy, and
Histologic Grade on the Survival of Patients with Intracranial
Astrocytomas
Francis G. Blankenberg, Raymond L. Teplitz, William Ellis, M. Shahriar Salamat, Byung Hee Min, Lisa Hall,
Derek B. Boothroyd, Iain M. Johnstone, and Dieter R. Enzmann
PURPOSE: To improve the prediction of individual survival in patients with intracranial astrocytomas through the analysis of volumetric tumor doubling time (VDt) and DNA ploidy. METHODS:
A pilot study was retrospectively conducted on a group of 25 patients with intracranial astrocytomas in whom recurrent and/or progressive disease was observed on serial contrast-enhanced CT
or MR examinations. VDt was computed using two or more data points from a semilogarithmic plot
of tumor volume versus time. Size-adjusted survival was calculated using a method based on VDt
and initial tumor volume to decrease the lead time bias attributable to differing tumor sizes at
presentation. RESULTS: Slower VDt was associated with significantly longer survival and sizeadjusted survival as determined by a univariate Cox proportional hazard analysis. Aneuploidy was
a significant indicator of poor survival. Aneuploid and multiclonal astrocytomas had poor sizeadjusted survivals compared with diploid astrocytomas. Grade IV astrocytomas had significantly
poorer survival and size-adjusted survival compared with lower grades (I to III), which individually
were not significantly correlated. However, grade IV histology was not a significant independent
predictor of size-adjusted survival in a multivariate Cox model, whereas VDt and DNA ploidy
remained significant. VDt also had a significant direct linear correlation to survival and sizeadjusted survival. CONCLUSIONS: VDt and DNA ploidy were more sensitive than histologic
grading as indicators of individual survival. Initial tumor size needs to be considered when staging
and assessing survival in patients with intracranial astrocytomas.
Index terms: Astrocytoma; Brain, neoplasms
AJNR Am J Neuroradiol 16:1001–1012, May 1995
The survival of patients with intracranial astrocytomas has been studied extensively with
respect to histologic grade, DNA ploidy, proliferative index (as measured by bromodeoxyuridine and thymidine labeling indices and flow
cytometry), and more recently by oncogene
analysis (1–21) in an attempt to improve prog-
Received February 17, 1994; accepted after revision December 14.
Sponsored by a grant from the Office of Technology and Licensing,
Stanford University, June 1990.
From the Department of Diagnostic Radiology, Stanford (Calif) University School of Medicine (F.G.B., D.R.E.); Departments of Statistics and
Health Research and Policy, Stanford University (D.B.B., I.M.J.); and Department of Medical Pathology, University of California at Davis, Sacramento (R.L.T., W.E., M.S.S., B.H.M., L.H.).
Address reprint requests to Francis G. Blankenberg, MD, Lucile Packard Children’s Hospital at Stanford, 725 Welch Rd, Stanford, CA 94304.
AJNR 16:1001–1012, May 1995 0195-6108/95/1605–1001
q American Society of Neuroradiology
nostic accuracy. Despite improved methods for
determining prognosis from histologic grading
of astrocytomas in groups of patients (1, 2), the
outlook for an individual patient has remained
uncertain. The use of DNA ploidy as measured
by flow cytometry and image cytometry in conjunction with histologic grade to predict individual survival is a subject of controversy in the
literature (3–11), and other studies have shown
an inconsistent relationship between labeling
indices of cellular proliferation and survival (12–
17).
Two studies have attempted to correlate
volumetric tumor doubling time (VDt) with histologic grade, with limited success (22, 23).
Our study focused on a group of 25 patients
with intracranial astrocytomas that radiographically demonstrated growth of the primary
and/or recurrent tumor after initial resection
1001
1002
BLANKENBERG
and adjuvant therapy. Our purpose was to correlate survival, DNA ploidy, and histologic
grade with VDt in an effort to improve prognostication and understanding of the cellular dynamics in patients with intracranial astrocytomas.
Materials and Methods
Patient and Specimen Selection
Twenty-five patients with intracranial astrocytomas
who had serial computed tomography (CT) or magnetic
resonance (MR) examinations demonstrating residual
and/or recurrent tumor were retrospectively studied in cooperation with the Division of Neuroradiology at Stanford
University Hospital and the Department of Pathology
(Neuropathology Section) of the University of California at
Davis. Twenty-four patients underwent primary resection
and/or diagnostic biopsy of their brain tumors from July
1979 to April 1991. One additional patient (patient 4) did
not undergo biopsy or therapy but was included, because
the clinical presentation, course, and radiographic appearance were consistent with a high-grade astrocytoma (glioblastoma multiforme). The average age was 43.5 years
with a range of 5 months to 76 years; there were a total of
15 female and 10 male patients; 23 patients had supratentorial astrocytomas, one a cerebellar astrocytoma, and
one a pontine astrocytoma.
Histology and DNA Image Cytometry
Eighteen patients had their primary histologic material
available for review by W.E. and S.S., who were blinded to
the results of previous pathologic interpretation, DNA
ploidy, VDt, and survival. Six patients were initially evaluated by the Division of Neuropathology at Stanford University Hospital; however, no paraffin-embedded tissue
from their primary biopsy or resection was available for
review. One patient (patient 4) did not undergo biopsy but
was included in the study as mentioned above. Histologic
grading followed the criteria of Dumas-Duport et al (1),
which emphasize the presence of mitoses, necrosis, and
endothelial proliferation. In this study, pilocytic astrocytomas were classified as grade I along with fibrillary astrocytomas that lacked all criteria for anaplasia. The designation gemistocytic astrocytoma indicated that the
majority of the neoplastic astrocytes had a gemistocytic
form. The reference histologic diagnosis used for each
case was based on the primary surgical biopsy and/or
resection. Seventeen patients had sufficient paraffinembedded material from their primary tumors for determination of DNA ploidy. DNA image cytometry was used for
the estimation of DNA ploidy in a technique described by
Teplitz et al (24). The DNA histograms were interpreted in
a blinded fashion by R.L.T. Studies were performed on
7-mm sections of suitable paraffin blocks, stained specifically for DNA by the Cell Analysis (CAS, Elmhurst, Ill)
procedure and examined with the CAS model 200 image
AJNR: 16, May 1995
cytometer. A 280-nm filter was used with a 20-nm band
pass and the CAS thickness correction program. To avoid
the possibility of detecting only clonal expansion within
these tumors, a minimum of 25 nuclei were analyzed on
four separate quadrants of each tumor. No cases were
included when the minimum number of determinations
(100 determinations) could not be obtained. In most cases
several hundred nuclei were quantitated. DNA ploidy results were classified in the following manner: D, diploid,
that is, normal somatic cell DNA content (7.18 pg/cell); E,
euploid, that is, diploid or an even multiple of diploid; A,
aneuploid, that is, abnormal somatic cell DNA content;
and MC, multiclonal, that is, two or more major clones.
Radiographic Tumor Volume Estimation and
Calculation of VDt
Eleven patients had contrast-enhanced serial CT examinations to determine residual and/or recurrent tumor
growth. Nine patients had serial MR examinations, five
with serial T1-weighted images (600 – 800/20/2 [repetition
time/echo time/excitations]) with or without gadolinium
enhancement and four with serial T2-weighted images,
(2000 –2500/30, 80/2), and five patients had a combination of contrast enhanced CT and/or MR T1-weighted images with or without gadopentetate dimeglumine. The
margins of only enhancing solid tumor tissue as seen on
CT or MR imaging were used for determination of tumor
volume. When only T2-weighted images were available,
vasogenic edema (ie, white matter edema) was not included in the volume determinations. Although the actual
margins were more difficult to determine on nonenhanced
T2-weighted MR images, we were able to define the bulk of
a tumor based on its abnormal signal and mass effect. A
similar set of methods for determination of tumor margins
for radiation therapy planning has been described by Galloway et al (25) and others (26, 27).
The calculation of the volume of gross tumor was done
retrospectively from the images of different scanners using
the method described by Breiman et al (28). Briefly, the
cross-sectional area of a lesion was calculated by planimetry. The absolute cross-sectional area of each square (in
centimeters) was determined from the centimeter scale on
the filmed image. Tumor volumes were calculated by multiplying the absolute cross-sectional area on each MR or
CT section by section thickness and summing the resultant products. To adjust for intersection gaps on MR scans,
the average cross-sectional area of two contiguous sections was multiplied by the section gap thickness; the
product was then added to the total volume. Tumor volumes were performed by F.B., who was blinded to the
histologic grade, DNA ploidy, and survival data.
Volumetric tumor doubling time of the residual primary
or recurrent disease was calculated using two or more data
points separated by at least 1 month from a semilogarithmic plot of tumor volume versus time as described by
Collins (29) and others (30 –32). Only periods in which
there was clear tumor progression demonstrated on serial
imaging studies before or between tumor resections were
AJNR: 16, May 1995
used for the calculation of VDt. Patients with three or more
data points had VDt calculated from the slope of the bestfit line generated by a simple linear regression. Ten patients had two serial volume determinations, eight had
three (r $.789), and two had six (r $.972). Five patients
had two or more periods of clinical progression or disease
recurrence separated by surgical resection and/or radiation therapy in which the resultant VDt of the recurrent
and/or residual disease of each time period was averaged.
The intervals in which it was possible to measure VDt were
as follows: 11 patients after primary resection and radiation therapy, three after a second resection, one after the
third resection, three after primary radiation therapy without resection, two before and after radiation therapy without resection, two after the primary and third resections,
one after the primary and second resections, and two
patients after radiation therapy only.
Size-adjusted survival was computed using a method
previously described by Collins et al (29) and others (30 –
32) to eliminate the lead-time bias for primary tumors of
differing sizes at diagnosis. The volume of each tumor at
diagnosis was converted into the approximate number of
tumor doublings from its theoretical origin as a single
neoplastic cell (assuming an average cell diameter of 10
mm). An arbitrary number of 30 tumor doublings (a 1-cmdiameter tumor) was subtracted from the observed volume
of each tumor at diagnosis (also expressed as the number
of tumor doublings). A volume of 30 doublings was chosen, because this usually represents the smallest size at
which a central nervous system tumor can be detected
clinically (33). This was then multiplied by VDt, and the
resultant product (ie, the extrapolated number of months
that were needed for a tumor to reach the observed size at
diagnosis from an initial size of 1 cm) was then added to
the observed survival to obtain size-adjusted survival. The
volume of tumor at death was extrapolated in a similar
fashion from the last radiographically determined tumor
volume after completion of all therapy to the time of death.
The formulas for the calculation of the number of tumor
doublings, size-adjusted survival, and estimated tumor
volume at death are given in the Appendix.
Statistical Analysis
Cox proportional hazard models were fitted for survival
and size-adjusted survival using various subsets of the
possible predictor variables as covariates. Likelihood ratio
tests were performed for assessing the significance of
models, whereas Wald statistics and coefficient/SE were
used to evaluate the significance of particular coefficients
in models involving more than one covariate by comparison with standard normal quantities. Survival analyses
were performed using S-PLUS software (Statistical Sciences). All P values are based on asymptotic approximations.
Survival, size-adjusted survival, VDt, and tumor volume
were all converted to natural logarithms before computation of their respective averages mentioned in the text
assuming log normal distributions for each of the above
quantities, according to Spratt et al (34, 35). The average
INTRACRANIAL ASTROCYTOMAS
1003
TABLE 1: Analysis of survival and size-adjusted survival with respect to VDt, histologic grade, and DNA ploidy
Univariate Models
Tumor growth rate
VDt
Histology
Grades I–IV
Grades I–III (excluding IV)
Grade IV (vs non–Grade IV)
DNA ploidy
Diploid, euploid, aneuploid,
and multiclonal
Aneuploid (coeff)*
Multiclonal (coeff)
Best-fit multivariant models
VDt and Grade IV
VDt (coeff)
Grade IV (coeff)
VDt and diploid
VDt (coeff)
Diploid (coeff)
Survival, P
.02
Size-adjusted
Survival, P
,.001
.007
.77, NS
.007
.03
.47, NS
.006
.14, NS
.007
.05
NS
.003
.02
.001
.04
.01
zzz
zzz
zzz
zzz
zzz
zzz
,.001
,.001
.03
* Coefficient of significance of a single variable in models involving
more than one covariate. NS indicates not significant.
values mentioned in the text represent the geometric
means of survival, size-adjusted survival, and VDt. Comparisons of averages (ie, geometric means) were performed using a two-tailed Student’s t test. Linear regressions of survival and size-adjusted survival on VDt were
calculated by the method of Buckley and James for regression with censored data, that is, patients still alive at
the completion of the study (36), using a function written
in S-PLUS by one of the authors (D.B.B.).
Results
Survival
Overall, VDt and the presence or absence of
grade IV histology were the most important predictors of (unadjusted) survival in the univariate
and as multivariate Cox models (Table 1).
Longer survival was seen in patients with longer
VDt (ie, slowly growing tumors), and shorter
survival was seen in patients with grade IV tumors. A univariate Cox model including only
grade I to III tumors, excluding grade IV astrocytomas, did not show any significant differences between the survival of each grade (nb,
patients evaluated as grades I–II were considered grade II in our analysis). The presence of
aneuploidy was of borderline significance with
respect to survival in a univariate model, but
this did not persist after the adjustment of the
other covariates in a multivariate model.
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AJNR: 16, May 1995
Fig 1. Relationship of survival time (solid triangle) and adjusted survival (inverted
triangle) in months, to VDt in days for each
patient. Also shown are fitted (BuckleyJames) regression lines for both survival responses. Censored patients (ie, patients
who were still alive at the end of the study)
are circled.
Size-Adjusted Survival
The analysis of size-adjusted survival was
performed on 24 of 25 patients, because one
patient (patient 6) did not have sufficient documentation of the size of the primary tumor available.
Overall, VDt and DNA ploidy were the most
important predictors of size-adjusted survival
both in the univariate and multivariate Cox
models; long VDt and tumor diploidy were correlated with a reduced hazard (see Table 1). The
presence or absence of grade IV histology was
of significance in a univariate model, but this
did not persist after adjusting for the other covariates in a multivariate model. In addition, a
univariate model including only grade I to III
astrocytomas did not reveal any significant dif-
ferences among the size-adjusted survivals of
each grade.
VDt and Tumor Volume
There was a significant linear relationship between VDt and survival (P 5 .0011) and also
with size-adjusted survival (P , .001) as shown
in Figure 1. The five patients who were alive at
the end of the study (censored data) were included in the analysis. The slopes of survival
and size-adjusted survival lines obtained using
Buckley and James’ method were 6.09 6 1.98
and 13.8 6 1.89 tumor doublings, respectively
(ie, number of tumor doublings 5 survival [or
size-adjusted survival]/VDt). More than one VDt
was able to be calculated in five patients at
AJNR: 16, May 1995
INTRACRANIAL ASTROCYTOMAS
1005
TABLE 2: Measurement of VDt during different clinical periods
Patient
Average VDt, d
8
70
13
92
17
181
22
349
25
556
VDt
75 d (2 points)
79 d (3 points, r 5 .878)
56 d (5 points, r 5 .789)
102 d (3 points, r 5 .971)
84 d (4 points, r 5 .936)
182 d (2 points)
181 d (2 points)
327 d (2 points)
370 d (4 points, r 5 .977)
530 d (4 points, r 5 .88)
582 d (3 points, r 5 .863)
Clinical Period
pre–radiation therapy (5/84–12/84)
7 mo after 1st radiation therapy (8/85–9/85)
2 mo after 2nd radiation therapy (12/85–5/86)
6 mo after 1st resection/radiation therapy (12/88–4/89)
1 mo after 2nd resection/radiation therapy (4/89–8/89)
during and immediately after radiation therapy (7/86–10/86)*
4 months after radiation therapy (1/87–8/87)
4 mo after 1st resection/radiation therapy (7/88–7/89)
5 mo after 3rd resection (7/90–12/91)
2 mo after 1st resection/radiation therapy (8/87–6/88)
1 mo after 3rd resection (7/89–4/91)
Note.—Patient 17 did not undergo a primary resection of tumor.
different periods of tumor progression (primary
or secondary tumor) as listed in Table 2. In
these patients, VDt of the primary or recurrent
disease changed little despite intervening resection and/or radiation therapy over a time interval ranging from 8 to 44 months as shown in
Figure 2.
Diploid and euploid tumors had a significantly longer average VDt (P , .001) compared
with aneuploid and multiclonal astrocytomas
(Table 3). No tumor in the diploid group had a
VDt of less than 84 days. Conversely, no tumor
of the aneuploid and multiclonal groups had a
VDt greater than 92 days (Table 4). Grade IV
Fig 2. Tumor volume measurements of patient 8 from diagnosis to death. XRT indicates radiation therapy.
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TABLE 3: Histologic grade and DNA ploidy correlated to VDt and tumor volume
Group
Average VDt, d
Average, in VDt
4.7 6 0.94, n 5 25 (4.65 6 0.82, n 5 16)*
4.98 6 0.93, n 5 9 (4.69 6 0.45, n 5 4)
4.94 6 1.25, n 5 7 (5.16 6 1.23, n 5 4)
4.24 6 0.77, n 5 9 (4.38 6 0.68, n 5 8)
5.19 6 0.59, n 5 11 (5.05 6 0.39, n 5 8)
3.79 6 0.60, n 5 6 (3.89 6 0.63, n 5 4)
All patients
Grades I–II
Grade III
Grade IV
Diploid and euploid
Aneuploid and multiclonal
110.3 (105)*
145 (108.3)
140 (173.7)
69.7 (80.4)†
179 (156)‡
44.3 (48.9)
Group
Average Tumor Volume, cm3
At diagnosis
Supratentorial astrocytomas
Grades I–II
Grade III
Grade IV
At death
Supratentorial astrocytomas
Grades I–II
Grade III
Grade IV
Average No. of Tumor Doublings
20.5 (22.1)*
19.2 (15.6)
19.2 (19.2)
26.6 (29.1)
35.3
35.2
35.2
35.7
6
6
6
6
2.4, n 5 22
2.29, n 5 8
3.48, n 5 6
1.66, n 5 8
181 (165)*
233 (165)
203 (203)
143.5 (143)
38.4
38.8
38.6
38.1
6
6
6
6
0.87,
1.31,
1.34,
1.26,
n
n
n
n
5
5
5
5
17
5
4
8
(35.4
(34.9
(35.2
(35.8
6
6
6
6
2.47, n 5 16)*
2.26, n 5 4)
4.2, n 5 4)
1.71, n 5 8)
(38.3
(38.3
(38.6
(38.1
6
6
6
6
1.08,
0.37,
1.34,
1.26,
n
n
n
n
5
5
5
5
16)*
4)
4)
8)
Note.—Numbers in parentheses are averages of the 16 patients with supratentorial gliomas with both preoperative and antemortem scans.
* Only 16 patients with supratentorial astrocytomas had scans available after last therapy before death in addition to scans before resection
and/or radiation therapy of the primary tumor.
† Not significantly different, P 5 .08 (P , .10) from grades I and II.
‡ Significantly different, P , .001 (P , .005) from the aneuploid and multiclonal group of astrocytomas.
tumors tended to have a shorter average VDt
than grade I and II astrocytomas, but this difference was not significant. In addition, there were
no significant differences between the average
VDt of grade IV tumors compared with grade III
tumors or non– grade IV tumors. The two infratentorial tumors in our study demonstrated similar sizes at diagnosis compared with cerebral
astrocytomas of approximately 35 tumor doublings. However, the two infratentorial astrocytomas demonstrated a markedly smaller final
tumor size at death of 35.3 tumor doublings
compared with the final volume of 38.4 tumor
doublings for the cerebral tumor group (see
Table 3).
Histologic Grade and DNA Ploidy
Of the 17 patients with DNA ploidy data, 6
patients (35.3%) had aneuploid or multiclonal
tumors, 2 (11.8%) had euploid tumors, and 9
(52.9%) had diploid tumors (see Table 4). Of
the seven patients with grade IV tumors, four
(57%) had aneuploid or multiclonal tumors with
an average VDt of 45.1 days, and three (43%)
were diploid with an average VDt of 151 days.
Of the four grade III patients, one (25%) had an
aneuploid tumor with a rapid VDt of 31 days,
one (25%) had a euploid tumor with a relatively
slow VDt of 291 days, and two (50%) were dip-
loid with an average VDt of 126.5 days. Of the
six grade I and II patients, one (17%) had a
multiclonal tumor with a relatively rapid VDt of
58 days, one (17%) had an euploid tumor with
an extremely slow VDt of 556 days, and four
(66%) were diploid with an average VDt of 161.6
days.
In the 12 patients in whom one or more biopsies were performed after initial resection, the
relationship of DNA ploidy and histology with
respect to time was unclear (Table 5). Generally
when tumors recurred and were subsequently
rebiopsied, they had progressed in histologic
grade and in the degree of aneuploidy and multiclonality. One patient (patient 2), who initially
had a grade IV tumor with an initially aneuploid
DNA histogram, converted to a grade III diploid
tumor after resection, radiation therapy, and
systemic chemotherapy.
Discussion
To gauge therapy and advise patients with
intracranial astrocytomas, an accurate measure
of prognosis is needed. Histologic grading has
not been adequate to determine individual outcome. Our study demonstrates that VDt and
DNA ploidy may be better prognosticators than
histologic grade. The importance of the growth
rate of residual or recurrent tumors in patients
AJNR: 16, May 1995
INTRACRANIAL ASTROCYTOMAS
1007
TABLE 4: Patients with intracranial astrocytomas
Patient (Age at
Diagnosis)
1(58 y)
2(28 y)
3(77 y)
4(72 y)
5(40 y)
6(36 y)
7(7 y)
8(52 y)
9(76 y)
10(43 y)
11(30 y)
12(8 mo)
13(50 y)
14(51 y)
15(67 y)
16(61 y)
17(71 y)
18(52 y)
19(62 y)
20(32 y)
21(35 y)
22(5 mo)
23(45 y)
24(23 y)
25(11 y)
Initial Histology before Therapy
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
IV
IV (gemistocytic)
III
IV*
III
II
I–II
I, oligodendro/astrocytoma
IV
IV
II
III
IV
IV
I
IV
IV
III (gemistocytic)
I
III
III
I, pilocytic
I–II (fibrillary)
III
II
Primary Tumor
Location
Survival, mo
Size-adjusted
Survival, mo
VDt, d
P
P
T
T
P
F/T/P
Pontine
F
T
P
F
T/SS
F
T/P
P/O
T
F/P
P
T
F
Cerebellar
SS
F
F(Bifrontal)
F
21.6
13.0
9
6.0
.18
61
9.7
31.3
2.5
14.1
23
.19.4
15.4
10.3
17.9
5.8
21.0
163
8.9
62.4
31.3
.69
.161
67
.67
24.9
19.1
8.3
9.9
.20
611
9.4
37.6
17.5
23.2
42.6
.39.5
38.4
29.4
35.5
53.6
48.0
195
52.3
144.9
102
.127
.202.5
210
.225
22
26
31
37
40
44
58
70
75
78
84
86
92
108
120
175
181
185
194
291
336
349
415
545
556
DNA Ploidy
MC D/T3T4
A Hypodiploid
A SubD/necrosis
zzz
zzz
zzz
MC D/T3Sub T3
zzz
zzz
MC D/A/H
D D/5.72% T4
D D/9/10% supra D
MC D/A/H
D D/11% - A
D D/6% supra T4
D D/a few .4N clones
D D/sub T3
D D/10% A
D D
E D/T4/6.79% hyper T4
zzz
D D
zzz
zzz
E E/,3% H
Note.—. indicates patient still alive; 1, unknown size of primary tumor; %, percentage of a particular subclone in the total population of nuclei
studied; MC, multiclonal tumor; A, aneuploid; D, diploid; T3, triploid; T4, tetraploid; E, euploid; H, hyperploid; F, frontal; P, parietal; O, occipital;
T, temporal; and SS, suprasellar.
* Probable histology based on radiographic appearance.
with intracranial astrocytomas is underscored
by the significance of VDt with respect to survival and size-adjusted survival. Furthermore,
there seems to be a significant direct relationship between VDt and survival as well as sizeadjusted survival based on our study. It is important to note, however, that our study dealt
with patients who were not cured by primary
therapy and who subsequently progressed or
developed recurrent disease, the imaging of
which allowed for the computation of VDt.
Therefore, our results cannot necessarily be
generalized to all patients with intracranial astrocytomas, particularly the lower-grade astrocytomas, which may be cured by simple excision and postoperative radiation therapy.
Hoshino et al (15) and others (16), although
concluding that both the size and the growth
rate of astrocytomas were important determinants of survival, thought that radiographically
determined VDt did not truly represent tumor
proliferative potential and, therefore, was not
prognostic. Several reasons were provided, one
of which was that astrocytomas tend to be
poorly marginated and that the entire extent of a
tumor cannot be reliably measured from CT
and/or MR. However, others suggest that the
determination of the location and volume of
gross tumor, however, can be reliably defined
by CT and/or MR (25–27). Furthermore, Yamashita and Kuwabara (22) found that the ratio
of tumor volumes of gross tumor estimated
from CT scanning was consistently similar to
the ratio of tumor volumes determined at surgery. Estimation of microscopic infiltration and
extension, manifested usually as nonspecific
peritumoral white matter edema, however, can
be challenging and, therefore, was not included
in our volume determinations.
A number of prior studies of radiographically
determined VDt (of primary and metastatic
breast and lung carcinoma) have demonstrated
the following: (a) that VDt is directly related to
survival, time to recurrence, and the percentage
of patients with recurrent disease at clinical follow-up; and (b) that VDt and survival are distributed in an exponential fashion in a patient
population (ie, both VDt and survival have log-
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TABLE 5: Histology and DNA ploidy in patients with one or more biopsies after initial resection
Patient
2
6
8
10
11
13
16
20
21
22
23
25
Pathologic
Specimen
Date
Histology
1st resection
2nd resection
1st resection
2nd resection
1st resection
2nd resection
1st resection
2nd resection
1st resection
2nd resection
1st resection
2nd resection
1st resection
2nd resection
1st resection
2nd resection
1st resection
2nd resection
1st resection
2nd resection
3rd resection
1st resection
2nd resection
3rd resection
4th resection
1st resection
2nd resection
12/87
4/88
1981
9/85
1/84
8/85
6/86
2/87
2/89
11/90
6/88
4/89
12/86
3/87
4/85
7/89
5/87
3/89
3/87
8/89
2/90
9/79
8/84
7/87
11/88
6/87
6/88
Grade IV
Grade III
Grade II
Grade IV
Grade I, oligodendro/astrocytoma
Grade III
Grade IV (gemistocytic)
Grade IV (gemistocytic)
Grade II
Grade IV
Grade IV
Grade IV
Grade IV
Grade IV
Grade III
Grade IV
Grade III
Grade III
Grade I, pilocytic
Grade I, pilocytic
Grade I, pilocytic
Grades I–II (fibrillary)
Grade III (fibrillary)
Grade III
Grade III
Grade II
Grade III
DNA Ploidy
A hypodiploid
D D
zzz
MC D/T4/A
zzz
zzz
MC D/A/H
zzz
D D/5.72% T4
MC D/4% A and H
MC D/A/H
zzz
D D/A few . 4N clones
MC D/T3/T4 ? octaploids
E D/T4/6.79% Hyper T4
MC D/T3/T4
zzz
zzz
D D
D D
zzz
zzz
D D/0.75% A
MC D/4.8% A and H
MC D/T4/A
E E (,3% H)
MC T3/T4/small supra T4 population
Note.—Abbreviations are as in Table 4.
normal frequency distributions) (37–53). Because tumor growth rate is also an exponential
function with respect to time, several authors
have concluded that survival is primarily dictated by VDt in patients in whom therapy is not
curative (50, 51). This hypothesis is bolstered
by the observation that VDt is directly proportional to survival and the time to recurrence as
noted in a recent critical review (54). Our current study establishes a link between radiographically determined VDt and survival in patients with intracranial astrocytomas.
A point worth emphasizing is that our data
both directly and indirectly demonstrate that
VDt must be relatively constant during the periods of clinical observation. When VDt was able
to be measured directly, over two or more periods of disease progression, it changed little
despite intervals between estimates of VDt of 8
or more months during which there was surgical
resection and/or radiation therapy. The slope
analysis of survival versus VDt as depicted in
Figure 1 provides an indirect confirmation of the
relative constancy of VDt over the clinical period of observation. If survival were linearly in-
dependent of VDt, then the slope of the best-fit
line generated by a linear regression analysis
would be zero. However, the slope of survival
versus VDt is 6.09 6 1.98 tumor doublings.
Stated slightly differently, the slope is greater
than 3 SD (P 5 .0011) above zero (ie, no linear
association between VDt and survival). The
slope of adjusted survival, 13.8 6 1.89 tumor
doublings (ie, greater than 6 SD from zero),
further underscores the fact that the linear relationship between VDt and survival in our study
is not coincidental.
The exceptions to the above were patients 6
and 18, who had unusually long survivals. Patient 6 initially had a grade II tumor, which recurred 5 years later as a rapidly enlarging mass
(VDt of 44 days), of which the patient quickly
died. Presumably the recurrent tumor was a distinctly different (ie, dedifferentiated) clone with
a rapid VDt compared with the original tumor.
Patient 18 had a relatively slowly growing grade
III astrocytoma (VDt of 185 days) who survived
for an exceptionally long period. Presumably
the initial therapy for this slowly growing tumor
was markedly more cytoreductive compared
AJNR: 16, May 1995
with other cases in this series. A marked degree
of cytoreduction coupled with a relatively slow
VDt could have accounted for a long survival.
At first glance our analysis seems to ignore
the effect of therapy (surgery, radiation therapy,
or chemotherapy); however, this is not the case.
In fact, the cumulative amount of cytoreduction
can be directly inferred when the VDt, tumor size
at diagnosis and at death, and survival are
known. For example, survival, as expressed as
the number of tumor doublings, should be equal
to the difference between the volume of tumor
at death and diagnosis, also expressed as the
number of tumor doublings, if no therapy was
undertaken. If these quantities are different (ie,
the patient survived more tumor doublings
than expected), then there must have been a
reduction of tumor volume due to therapy in
which the patient gained x number of tumor
doubling times (x 5 survival [number of doublings] 2 tumor volume at death [number
of doublings] 2 tumor volume at diagnosis
[number of doublings]). Therefore, the average
gain in number of tumor doubling times in our
group was three tumor doublings (3.0 doublings 5 6.09 doublings [slope] 2 38.4 doublings [volume at death] 2 35.3 doublings
[volume at diagnosis]). This gain is equivalent
to a 90% reduction in tumor volume. Because
the average VDt in our study was 110 days,
the therapeutic gain of three doubling times is
equal to 1 year of extended survival. The gain,
in terms of time, however, would be greater
for patients with longer VDts and far less for
the rapidly growing (shorter-VDt) tumors.
These arguments apply only to cerebral astrocytomas in which mass effect is usually the
cause of death. The two infratentorial tumors in
our group were similar to each other in size at
the time of diagnosis and at the time of death,
which may indicate that the invasion of vital
brain stem structures by recurrent disease, not
gross mass effect, was the cause of death.
In an individual patient, the benefit of a single
therapeutic intervention can be estimated from
the following example regardless of its anatomic location. For example, if a patient has an
intracranial astrocytoma with an initial tumor
volume of 30 VDts (0.523 cm3) growing at a
VDt of 1 month, which recurs with a volume of
30 VDts 12 months after resection, then the
reduction of tumor burden must have been
equivalent to 12 VDts. A 12-VDt decrease in
tumor burden is equivalent to an approximately
INTRACRANIAL ASTROCYTOMAS
1009
0.999% reduction in tumor volume (ie, less than
0.0005 cm3 of residual tumor after resection),
which would be undetectable when the patient
is scanned in the immediate postoperative
period.
A surprising result of our study was the relative insensitivity of histologic grade with respect
to survival. In a multivariate analysis, histology
only became a significant independent predictor of survival if grade IV was compared with
non– grade IV tumors. In contrast, VDt (a continuous variable) based on a multivariant analysis was a highly significant independent predictor of survival. In addition, histology ceased
to be a significant independent predictor as
shown by the multivariate analysis of histology,
DNA ploidy, and VDt with respect to size-adjusted survival. Histologic grade is clearly significant in large registry-based studies (1, 9,
10). Based on our study, however, histology is a
relatively insensitive predictor of survival with
respect to VDt and requires relatively large patient populations to see significant differences
between individual grades.
One possible bias not explored in our study
was the use of the histologic grade of the primary tumor as the reference diagnosis for each
case. VDt, on the other hand, was determined
from a period(s) of progression of the primary
tumor or from the growth of recurrent tumor
sometime after initial diagnosis. As stated previously, VDt in our patient population was relatively constant from diagnosis to death. In contrast, in the 12 patients with two or more
follow-up biopsies, 6 increased in histologic
grade, and 1 decreased. Furthermore, in two of
the five patients with two or more measurements of VDt at different clinical periods (patients 8 and 25), histologic grade increased,
whereas VDt remained constant. Because of the
changes of histologic grade over time and with
therapy, it is unlikely that the grade of recurrent
disease would be as helpful as VDt in the prediction of survival, although this issue was not
directly addressed in our study.
The relationship between DNA ploidy and
survival has been a subject of controversy in the
literature. One large study (10, 11) claims a
significantly longer survival in patients with hypertriploid DNA histograms, whereas another
large series (9) claims a significantly poorer
survival in patients with aneuploid and multiclonal tumors. Our study showed that aneuploid
and multiclonal tumors had a significantly
1010
BLANKENBERG
shorter survival than the remainder of the group
only in the univariate analysis (see Table 1). An
aneuploid and multiclonal DNA histogram was
not a significant independent predictor of survival as shown in a multivariate analysis. The
differences in the various studies of DNA ploidy
may in part be attributable to the lack of correction for the lead time bias because of differing tumor sizes at diagnosis. We, therefore, attempted to decrease lead time bias by the
calculation of size-adjusted survival, thereby establishing a baseline tumor volume (a 1-cmdiameter tumor) from which the survival of patients could be more reasonably compared.
When size-adjusted survival was used in place
of survival, DNA ploidy (diploid and euploid
versus aneuploid and multiclonal) became a
highly significant independent variable as
shown by a multivariate analysis. The identification of patients destined to have poor survival
within each histologic grade was also possible
through the analysis of DNA ploidy (as well as
VDt). Furthermore, we found that aneuploid and
multiclonal tumors in our study grew significantly faster than the diploid and euploid tumors. This conceivably could be another confounding factor in correlating DNA ploidy with
survival if the issue of lead time bias because of
differing tumor sizes at diagnosis is not addressed. The lead time bias in our study ranged
from 0 to 12.7 years with an average lead time
of 2.3 years.
DNA ploidy and histologic grade, however,
progressed with time as seen with multiple sequential biopsies with one exception. The exception may have been attributable to sampling
or to radiation therapy and chemotherapy,
which can be expected to select against the
aneuploid clones of the tumor, leaving the diploid clones as in other malignancies (55). Timing, therefore, seems to be a critical factor in
obtaining the most predictive value from estimates of DNA ploidy. Analysis of the primary
tumor tissue before therapy correlates best with
survival. The frequency of aneuploid tumors
also increased with higher histologic grades as
noted by Zaprianov and Christov (6), Ahayi (3),
and others (7–11). In addition, these authors
also noted the same relationships of DNA
ploidy, histologic grade, timing of biopsied material, and survival as were found in our study.
With the exception of the study by Zaprianov
and Christov (6), another problem with previous
studies is that flow cytometry or image cytom-
AJNR: 16, May 1995
etry (after tumor disaggregation and preparation of nuclei) were used to estimate DNA
ploidy. When performing flow cytometry, tumor
cells are not separated from normal cells, and
the estimates of DNA ploidy may, therefore, be
unreliable, as noted in two critical reviews (56,
57). A similar problem may also occur when
nuclei analyzed by image cytometry are prepared from suspensions (11). In this type of
preparation, distinction between normal and
pathologic isolated nuclei may be uncertain.
Conclusions
VDt and tumor size are important prognostic
variables in patients with intracranial astrocytomas who have recurrent or progressive disease.
VDt demonstrated a significant direct linear relationship to survival as well as size-adjusted
survival and, therefore, is generally predictive of
an individual astrocytoma patient’s prognosis.
DNA ploidy also becomes significant when survival is adjusted for tumor size at presentation.
Histologic grade is a relatively insensitive predictor of individual survival compared with in
vivo tumor growth rate (VDt). Based on our
results, we recommend that VDt and DNA
ploidy as well as primary tumor size be further
studied to refine current staging as well as the
assessment of therapy in patients with intracranial astrocytomas.
Appendix
The method of Collins et al (29) was used to calculate
tumor volume in terms of the number of tumor doublings
from a single neoplastic cell origin (with an average diameter of 10 mm) assuming exponential tumor growth.
Briefly, a 1-cm-diameter tumor has a volume of 0.523
cm3, which corresponds to 230 cells or 30 tumor doublings. Therefore:
230 cells
0.523 cm3
5
2x cells
observed tumor volume (cm3),
where x represents the number of tumor doublings. Solving for x:
1)
x 5 30 1
ln (observed tumor volume (cm3)
ln 2
,
where ln is a natural logarithm, and ln 2 ' 0.693.
Adjusted survival was calculated using the formula:
2)
adjusted survival 5 ~x 2 30! 3 ~VDt)
1 observed survival,
AJNR: 16, May 1995
INTRACRANIAL ASTROCYTOMAS
where x represents the observed tumor volume at diagnosis expressed as the number of tumor doublings as calculated from equation 1.
Tumor volume at death was determined by first calculating the number of months from the last imaging study
until death and dividing by VDt (in months). This was then
added to the last observed tumor volume (also as expressed as the number of tumor doublings) to obtain the
estimated tumor volume at death. The estimated tumor
volume at death was then converted into units of cubic
centimeters by the following relationship:
3)
tumor volume(cm3) 5
2z cells
230 cells
3 (0.523 cm3),
where z is the estimated tumor volume at death in terms of
the number of tumor doublings.
Acknowledgments
We thank Jerry Halpern, PhD, for helpful discussions
concerning Buckley and James censored regression. We
also thank Lela Terrazas for preparation of the tables and
figures used in the manuscript.
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Please see the commentary on page 1013 in this issue.